In waveform design for magnetic resonance applications, periodic continuous-wave excitation offers potential advantages that remain largely unexplored because of a lack of understanding of the Bloch equation with periodic continuous-wave excitations. Using harmonic balancing techniques the steady state solutions of the Bloch equation with periodic excitation can be effectively solved. Moreover, the convergence speed of the proposed series approximation is such that a few terms in the series expansion suffice to obtain a very accurate description of the steady state solution. The accuracy of the proposed analytic approximate series solution is verified using both a simulation study as well as experimental data derived from a spherical phantom with doped water under continuous-wave excitation. Typically a five term series suffices to achieve a relative error of less than one percent, allowing for a very effective and efficient analytical design process. The opportunities for Rabi frequency modulated continuous-wave form excitation are then explored, based on a comparison with steady state free precession pulse sequences.

Estimation of multiple T2 components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T2 model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T2 component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T2 spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.

Recently there has been increasing interest in estimating the distribution of relaxation times contributing to a magnetic resonance signal. This paper shows that it is impractical to estimate the spread of such a distribution from typical measurements. Instead, a Bayesian estimator is developed for a discrete distribution, which is very robust to noise. Although the distribution spread is not modelled, the estimates capture the main features of the distribution such as the mode locations and often provide improved myelin water fraction estimates in simulation examples.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

Traditional magnetic resonance imaging (MRI) studies are based on image contrast and qualitative analysis. However, there is an increasing interest in quantifying the physical parameters of the object such as the free induction decay rate, T*2. In this paper, a new Bayesian algorithm is proposed for the estimation of T*2from gradient echo MRI scans. Current estimation methods use a simple signal model based on Fourier reconstruction which imposes a trade-off between the signal-to-noise ratio (SNR) and image distortion, and results in estimation bias. The proposed algorithm uses a Gibbs sampler in a Bayesian framework to account for image distortion allowing data samples to be acquired with increased SNR, improving the estimation accuracy. Estimation results on simulated objects and in vivo experimental data demonstrate the effectiveness of the algorithm.

We present a computationally efficient algorithm that minimizes the transmission energy and latency associated with transmitting a file across a Gilbert Elliott fading channel. We formulate the optimal tradeoff between transmission energy and latency as a partially observed Markov decision process problem (POMDP). The channel state is not directly observed and hence transmission decisions must be based on ACK/NAK information provided over a feedback channel. The key idea is to reformulate the resulting POMDP as a Markovian search problem, with optimal transmission control policies that are threshold in nature. Threshold policies are computationally inexpensive to implement. Our analysis shows that for different parameter values of the Gilbert Elliott fading channel, the optimal transmission policy, while threshold in structure, exhibits vastly different behaviour - from persistent retransmission to back-off and wait. Numerical examples demonstrate the performance improvements that can be obtained using the optimal threshold policies as compared to existing heuristic algorithms.

We derive stochastic control algorithms to achieve the optimal tradeoff between throughput and energy consumption for transmitting packets across a time varying wireless channel with memory. The channel state is not directly observed and hence transmission decisions must be based on ACK/NAK information provided over a feedback channel. By reformulating the problem as a Markovian search problem, we propose a conjecture that the optimal transmission control policies are threshold in nature. Threshold policies are computationally inexpensive to implement. Numerical simulations demonstrate the performance improvements that can be obtained using the optimal threshold policies as compared to heuristic algorithms.

Conventional approaches to perceptual grouping assume little specific knowledge about the object(s) of interest. However, there are many applications in which such knowledge is available and useful. Here, we address the problem of finding the bounding contour of an object in an image when some prior knowledge about the object is available. We introduce a framework for combining prior probabilistic knowledge of the appearance of the object with probabilistic models for contour grouping. A constructive search technique is used to compute candidate closed object boundaries, which are then evaluated by combining figure, ground, and prior probabilities to compute the maximum a posteriori estimate. A significant advantage of our formulation is that it rigorously combines probabilistic local cues with important global constraints such as simplicity (no self-intersections), closure, completeness, and nontrivial scale priors. We apply this approach to the problem of computing exact lake boundaries from satellite imagery, given approximate prior knowledge from an existing digital database. We quantitatively evaluate the performance of our algorithm and find that it exceeds the performance of human mapping experts and a competing active contour approach, even with relatively weak prior knowledge. While the priors may be task-specific, the approach is general, as we demonstrate by applying it to a completely different problem: the computation of human skin boundaries in natural imagery.

"track-before-detect" (TBD) is a target tracking technique where the data is processed over a number of frames before decisions on target existence are made. The aim of this paper is to use extreme value theory to analyse the performance of a dynamic programming based TBD algorithms. Asymptotic expressions are obtained for the false alarm and track detection probabilities using extremal analysis of limiting distributions. Apart from fitting the simulated results far more accurately than previous works in the TBD literature, our analysis does not require the unrealistic assumptions of independence and Gaussianity.

We present a finite dimensional iterative algorithm for optimal maximum a posteriori (MAP) state estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. We show that several bilinear models previously considered in the literature are special cases of the general bilinear model we propose. Our iterative algorithm for state estimation is based on the expectation-maximization (EM) algorithm and outperforms the widely used extended Kalman filter (EKF). Unlike the EKF our algorithm is an optimal (in the MAP sense) finite-dimensional solution to the state sequence estimation problem for bilinear models.

This paper presents a novel nonlinear estimation algorithm based on hidden Markov models for narrowband interference suppression in CDMA spread spectrum systems. The proposed algorithm combines a recursive hidden Markov model estimator, a Kalman filter and a recursive prediction error parameter estimation algorithm. It is shown that the proposed algorithm not only outperforms the nonlinear filtering techniques for narrowband interference suppression presented in Rusch and Poor (1994), but that it outperforms and has faster, more robust convergence properties than the cross-coupled expectation maximization based algorithm presented in Logothetis and Krishnamurthy.